• Korean Journal of Mathematics
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• 제29권3호
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• pp.613-620
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• 2021

In this paper, we introduce the definition of weakly convergent sequence in fuzzy normed spaces. We investigate relationship between convergent sequence and weakly convergent sequence in fuzzy normed spaces. We also study the dual spaces of a standard fuzzy normed space and 01-fuzzy normed space.

• 충청수학회지
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• 제5권1호
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• pp.173-183
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• 1992

In this paper, we introduce the notion of the weakly 2-convergence and strongly 2-convergence for 2-metric spaces. And we investigate its properties and prove the closedness and convexity of T(z,y, z).

• 대한수학회보
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• 제22권1호
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• pp.23-29
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• 1985

Let H be an arbitrary complex Hilbert space. We constructed an extension K of H by means of weakly convergent sequences in H and the Banach limit. Let .phi. be the faithful *-representation of L(H) on K. In this note, we investigated the relations between spectra of T in L(H) and .phi.(T) in L(K) and we obtained the following results: 1) If T is a compact operator on H, then .phi.(T) is also a compact operator on K (Proposition 6), 2) .sigma.$_{l}$ (.phi.(T)).contnd..sigma.$_{l}$ (T) for any operator T.mem.L(H) (Corollary 10), 3) For every operator T.mem.L(H), .sigma.$_{ap}$ (.phi.(T))=.sigma.$_{ap}$ (T))=.sigma.$_{ap}$ (T)=.sigma.$_{p}$(.phi.(T)) (Lemma 12, 13) and .sigma.$_{c}$(.phi.(T))=.sigma.(Theorem 15).15).